Study On Robust Parameter Estimation And Model Selection Method In Longitudinal Data Analysis

This paper focuses on the model selection in the longitudinal data analysis, including the robust estimates, covariate selection and working correlation matrix selection.Firstly, to yield more efficient and robust parameter estimation and improve the performance of variable selection in regression simultaneously, we propose a new weighted version of the LAD-LASSO method based on the HBR weights(denoted as HWLAD-LASSO). The HWLAD-LASSO estimator is proved to enjoy the oracle properties and its superiority over the typical WLAD-LASSO method is demonstrated by simulation study and a real example.Secondly, AIC and BIC based on either empirical likelihood(denoted as EAIC and EBIC) or Gaussian pseudo-likelihood(denoted as GAIC and GBIC) have been proposed to select correlation structure in longitudinal data analysis. This paper evaluates the performance of EAIC, EBIC, GAIC, and GBIC in selecting regression variables in the framework of the well known generalized estimating equations via intensive simulation studies. Our findings are(i) GAIC and GBIC outperform other existing methods in selecting regression variables;(ii) EAIC and EBIC are effective in selecting covariates only when the working correlation structure is correctly specified; and(iii) GAIC and GBIC are robust, which means that they perform well regardless the working correlation structure is correctly specified or not. We also briefly illustrate using a epilepsy dataset.Finally, a new robust variable selection approach is introduced in this paper by combining the efficient and robust generalized estimating equations and adaptive LASSO penalty function(denoted as AL-ERGEE) for longitudinal generalized linear models. Then, an efficient weighted Gaussian pseudo-likelihood version of the BIC(denoted as WGBIC) is proposed to choose the tuning parameter in the process of robust variable selection and to select the best working correlation matrix simultaneously. Meanwhile, the oracle properties of the proposed robust variable selection method are established and an efficient algorithm combining the iterative weighted least squares and Minorization-Maximization is proposed to implement the AL-ERGEE's numerical solution. Simulation studies and a real dataset analysis are carried out to demonstrate the following results:(i) the proposed robust variable selection method is very efficient and have quite good performance, especially when the tuning parameter is specified via WGBIC instead of the GCV criterion, such as better variable selection and extremely high accuracy of correlation matrix selection;(ii) the proposed method is able to accommodate the effect of outliers for both the variable selection and working correlation matrix selection.